Games like Metamorphic
Games like Metamorphic include Portal, Viewfinder, LIMBO, Papers, Please, and Poly Bridge. We matched them by the tags players give Metamorphic on Steam (Simulation, Indie, Puzzle, First-Person, and Physics): closest matches first, and among equally close ones the better-known games.

Portal
Shared: Puzzle · First-Person · Puzzle Platformer

Viewfinder
Shared: Puzzle · First-Person · Puzzle Platformer

LIMBO
Shared: Indie · Puzzle · Puzzle Platformer

Papers, Please
Shared: Simulation · Indie · Puzzle

Poly Bridge
Shared: Simulation · Puzzle · Physics

Portal 2
Shared: Puzzle · First-Person · Puzzle Platformer

Surgeon Simulator
Shared: Simulation · Physics · Indie

The Talos Principle
Shared: Puzzle · First-Person · Atmospheric

Human Fall Flat
Shared: Puzzle · Physics · Puzzle Platformer

Heavenly Bodies
Shared: Physics · Simulation · Puzzle

Antichamber
Shared: Puzzle · Indie · First-Person

The Witness
Shared: Puzzle · First-Person · Indie

Besiege
Shared: Simulation · Physics · Puzzle

Supraland
Shared: Puzzle Platformer · First-Person · Puzzle

Little Nightmares
Shared: Atmospheric · Puzzle · Indie

Cyber Manhunt
Shared: Simulation · Puzzle · Indie

Viscera Cleanup Detail
Shared: Simulation · First-Person · Indie

INSIDE
Shared: Atmospheric · Indie · Puzzle Platformer

Return of the Obra Dinn
Shared: Puzzle · Indie · Atmospheric

Garry's Mod
Shared: Physics · First-Person · Simulation

The Room
Shared: Puzzle · Atmospheric · Indie

Superliminal
Shared: Puzzle · First-Person · Physics

BONEWORKS
Shared: Physics · Puzzle · First-Person

Isonzo
Shared: Simulation · Indie · Atmospheric